Download 4 Newton`s First Law of Motion—Inertia

4 Newton’s First Law of Motion—Inertia
Forces cause changes
in motion.
4 Newton’s First Law of Motion—Inertia
A ball at rest in the middle of a
flat field is in equilibrium. No net
force acts on it.
If you saw it begin to move
across the ground, you’d look
for forces that don’t balance to
zero.
We don’t believe that changes in
motion occur without cause.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Natural motion on Earth was thought to be either
straight up or straight down.
• Objects seek their natural resting places:
boulders on the ground and smoke high in the air
like the clouds.
• Heavy things fall and very light things rise.
• Circular motion was natural for the heavens.
• These motions were considered natural–not
caused by forces.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Violent motion, on the other hand, was imposed
motion.
• It was the result of forces that pushed or pulled.
• The important thing about defining violent motion
was that it had an external cause.
• Violent motion was imparted to objects.
• Objects in their natural resting places could not
move by themselves.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Boulders do not move without cause.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
It was commonly thought for nearly 2000 years that a force
was responsible for an object moving “against its nature.”
• The state of objects was one of rest unless they were
being pushed or pulled or moving toward their natural
resting place.
• Most thinkers before the 1500s considered it obvious
that Earth must be in its natural resting place.
• A force large enough to move it was unthinkable.
• Earth did not move.
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
According to Aristotle, what were the
two types of motion?
4 Newton’s First Law of Motion—Inertia
4.1 Aristotle on Motion
Aristotle, the foremost Greek scientist,
studied motion and divided it into two
types: natural motion and violent motion.
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
The astronomer Nicolaus Copernicus (1473–1543)
formulated a theory of the moving Earth.
This idea was extremely controversial at the time. People
preferred to believe that Earth was at the center of the
universe.
Copernicus worked on his ideas in secret. The first copy of
his work, De Revolutionibus, reached him on the day of his
death, May 24, 1543.
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
Nicolaus Copernicus
proposed that Earth moved
around the sun.
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
What did Copernicus state about
Earth’s motion?
4 Newton’s First Law of Motion—Inertia
4.2 Copernicus and the Moving Earth
Copernicus reasoned that the simplest way
to interpret astronomical observations was
to assume that Earth and the other planets
move around the sun.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo, the foremost scientist of late-Renaissance Italy, was
outspoken in his support of Copernicus.
One of Galileo’s great contributions to physics was
demolishing the notion that a force is necessary to keep an
object moving.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Friction is the name given to the force that acts between
materials that touch as they move past each other.
• Friction is caused by the irregularities in the surfaces of
objects that are touching.
• Even very smooth surfaces have microscopic
irregularities that obstruct motion.
• If friction were absent, a moving object would need no
force whatever to remain in motion.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo tested his idea by rolling balls along plane surfaces
tilted at different angles.
• A ball rolling down an inclined plane speeds up.
• A ball rolling up an inclined plane—in a direction
opposed by gravity—slows down.
• A ball rolling on a smooth horizontal plane has almost
constant velocity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. Downward, the ball moves with Earth’s gravity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. Downward, the ball moves with Earth’s gravity.
b. Upward, the ball moves against gravity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. Downward, the ball moves with Earth’s gravity.
b. Upward, the ball moves against gravity.
c. On a level plane, it does not move with or against gravity.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo stated that if friction were entirely absent, a ball
moving horizontally would move forever.
No push or pull would be required to keep it moving once it
is set in motion.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo’s conclusion was supported by another line of
reasoning.
• He described two inclined planes facing each other.
• A ball released to roll down one plane would roll up the
other to reach nearly the same height.
• The ball tended to attain the same height, even when
the second plane was longer and inclined at a smaller
angle than the first plane.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. The ball rolling down the incline rolls up the opposite
incline and reaches its initial height.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. The ball rolling down the incline rolls up the opposite
incline and reaches its initial height.
b. The ball rolls a greater distance to reach its initial height.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
a. The ball rolling down the incline rolls up the opposite
incline and reaches its initial height.
b. The ball rolls a greater distance to reach its initial height.
c. If there is no friction, the ball will never stop.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
If the angle of incline of the second plane were reduced to
zero so that the plane was perfectly horizontal, only friction
would keep it from rolling forever.
It was not the nature of the ball to come to rest as Aristotle
had claimed.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo stated that this tendency of a moving body to keep
moving is natural and that every material object resists
changes to its state of motion.
The property of a body to resist changes to its state of
motion is called inertia.
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
think!
A ball is rolled across a counter top and rolls slowly to a stop.
How would Aristotle interpret this behavior? How would
Galileo interpret it? How would you interpret it?
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
think!
A ball is rolled across a counter top and rolls slowly to a stop.
How would Aristotle interpret this behavior? How would
Galileo interpret it? How would you interpret it?
Answer: Aristotle would probably say that the ball stops
because it seeks its natural state of rest. Galileo would
probably say that the friction between the ball and the table
overcomes the ball’s natural tendency to continue rolling—
overcomes the ball’s inertia—and brings it to a stop. Only you
can answer the last question!
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
According to Galileo, when is a force
needed to keep an object moving?
4 Newton’s First Law of Motion—Inertia
4.3 Galileo on Motion
Galileo argued that only when friction is
present—as it usually is—is a force needed
to keep an object moving.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Newton’s first law, usually called the law of inertia, is a
restatement of Galileo’s idea that a force is not needed to
keep an object moving.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Objects at Rest
Simply put, things tend to keep on doing what they’re
already doing.
• Objects in a state of rest tend to remain at rest.
• Only a force will change that state.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Objects at rest tend to remain at rest.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Objects in Motion
Now consider an object in motion.
• In the absence of forces, a moving object tends
to move in a straight line indefinitely.
• Toss an object from a space station located in
the vacuum of outer space, and the object will
move forever due to inertia.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Blasts of air from many tiny holes provide a nearly friction-free
surface on the air table. If you slide a hockey puck along the
surface of a city street, the puck soon comes to rest. If you
slide it along an air table where friction is practically absent, it
slides with no apparent loss in speed.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
The law of inertia provides a completely
different way of viewing motion from the
ancients.
• Objects continue to move by
themselves.
• Forces are needed to overcome
any friction that may be present and
to set objects in motion initially.
• Once the object is moving in a
force-free environment, it will move
in a straight line indefinitely.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
A force of gravity between the sun and its planets holds
the planets in orbit around the sun. If that force of gravity
suddenly disappeared, in what kind of path would the
planets move?
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
A force of gravity between the sun and its planets holds
the planets in orbit around the sun. If that force of gravity
suddenly disappeared, in what kind of path would the
planets move?
Answer: Each planet would move in a straight line at
constant speed.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
Is it correct to say that the reason an object resists change
and persists in its state of motion is that it has inertia?
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
think!
Is it correct to say that the reason an object resists change
and persists in its state of motion is that it has inertia?
Answer: We don’t know the reason why objects persist in
their motion when nothing acts on them, but we know that
they do, and we call this property inertia.
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
What is Newton’s first law of motion?
4 Newton’s First Law of Motion—Inertia
4.4 Newton’s Law of Inertia
Newton’s first law states that every object
continues in a state of rest, or of uniform
speed in a straight line, unless acted on by
a nonzero net force.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The amount of inertia an object has depends on its mass—
which is roughly the amount of material present in the object.
Mass is a measure of the inertia of an object.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
You can tell how much matter is in a can when you kick it.
Kick an empty can and it moves. Kick a can filled with sand
and it doesn’t move as much.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Not Volume
Do not confuse mass and volume.
• Volume is a measure of space and is
measured in units such as cubic
centimeters, cubic meters, and liters.
• Mass is measured in the fundamental unit
of kilograms.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Which has more mass, a feather pillow or a common
automobile battery?
Clearly an automobile battery is more difficult to set into
motion. This is evidence of the battery’s greater inertia and
hence its greater mass.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The pillow has a larger size (volume) but a smaller
mass than the battery.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Not Weight
Mass is often confused with weight.
• We often determine the amount of
matter in an object by measuring
its gravitational attraction to Earth.
However, mass is more
fundamental than weight.
• Mass is a measure of the amount
of material in an object. Weight,
on the other hand, is a measure
of the gravitational force acting on
the object.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass Is Inertia
The amount of material in a particular stone is the
same whether the stone is located on Earth, on the
moon, or in outer space.
• The mass of the stone is the same in all of
these locations.
• The weight of the stone would be very different
on Earth and on the moon, and still different in
outer space.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The stone’s inertia, or mass, is a property of the stone and
not its location.
The same force would be required to shake the stone with
the same rhythm whether the stone was on Earth, on the
moon, or in a force-free region of outer space.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
It’s just as difficult to
shake a stone in its
weightless state in
space as it is in its
weighted state on
Earth.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
We can define mass and weight as follows:
• Mass is the quantity of matter in an object. More
specifically, mass is a measure of the inertia, or
“laziness,” that an object exhibits in response to any
effort made to start it, stop it, or otherwise change its
state of motion.
• Weight is the force of gravity on an object.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
Mass and weight are proportional to each other in a
given place:
• In the same location, twice the mass weighs twice
as much.
• Mass and weight are proportional to each other,
but they are not equal to each other.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
One Kilogram Weighs 10 Newtons
It is common to describe the amount of matter in an
object by its gravitational pull to Earth, that is, by its
weight.
• In the United States, the traditional unit of
weight is the pound. In most parts of the world,
however, the measure of matter is commonly
expressed in units of mass, the kilogram (kg).
• At Earth’s surface, 1 kilogram has a weight of
2.2 pounds.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The SI unit of force is the newton. The SI symbol for the
newton is N.
One newton is equal to slightly less than a quarter
pound.
If you know the mass of something in kilograms and
want its weight in newtons at Earth’s surface, multiply
the number of kilograms by 10.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
One kilogram of nails weighs 10
newtons, which is equal to 2.2
pounds. Away from Earth’s
surface, where the force of
gravity is less, the bag of nails
weighs less.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
think!
Does a 2-kilogram bunch of bananas have twice as much
inertia as a 1-kilogram loaf of bread? Twice as much mass?
Twice as much volume? Twice as much weight, when
weighed in the same location?
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
think!
Does a 2-kilogram bunch of bananas have twice as much
inertia as a 1-kilogram loaf of bread? Twice as much mass?
Twice as much volume? Twice as much weight, when
weighed in the same location?
Answer: Two kilograms of anything has twice the inertia and
twice the mass of one kilogram of anything else. In the same
location, where mass and weight are proportional, two
kilograms of anything will weigh twice as much as one
kilogram of anything. Except for volume, the answer to all the
questions is yes. Bananas are much more dense than bread,
so two kilograms of bananas must occupy less volume than
one kilogram of bread.
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
What is the relationship between mass
and inertia?
4 Newton’s First Law of Motion—Inertia
4.5 Mass—A Measure of Inertia
The more mass an object has, the greater
its inertia and the more force it takes to
change its state of motion.
4 Newton’s First Law of Motion—Inertia
An object in mechanical
equilibrium is stable, without
changes in motion.
4 Newton’s First Law of Motion—Inertia
Things that are in balance with one
another illustrate equilibrium.
Things in mechanical equilibrium are
stable, without changes of motion.
The rocks are in mechanical equilibrium.
An unbalanced external force would be
needed to change their resting state.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
A force is a push or a pull.
A force of some kind is always required to change the
state of motion of an object.
The combination of all forces acting on an object is
called the net force. The net force on an object
changes its motion.
The scientific unit of force is the newton, abbreviated N.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
The net force depends on
the magnitudes and
directions of the applied
forces.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Net Force
When the girl holds the
rock with as much force
upward as gravity pulls
downward, the net force
on the rock is zero.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Tension and Weight
A stretched spring is under a “stretching force”
called tension.
Pounds and newtons are units of weight, which
are units of force.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Tension and Weight
The upward tension in the
string has the same magnitude
as the weight of the bag, so the
net force on the bag is zero.
The bag of sugar is attracted to
Earth with a gravitational force
of 2 pounds or 9 newtons.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Tension and Weight
The upward tension in the
string has the same magnitude
as the weight of the bag, so the
net force on the bag is zero.
The bag of sugar is attracted to
Earth with a gravitational force
of 2 pounds or 9 newtons.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Tension and Weight
There are two forces acting on the bag of sugar:
• tension force acting upward
• weight acting downward
The two forces on the bag are equal and opposite. The
net force on the bag is zero, so it remains at rest.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Force Vectors
A vector is an arrow that represents the magnitude and
direction of a quantity.
A vector quantity needs both magnitude and direction for a
complete description. Force is an example of a vector quantity.
A scalar quantity can be described by magnitude only and
has no direction. Time, area, and volume are scalar quantities.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Force Vectors
This vector represents a force of 60 N to the right.
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
Force Vectors
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
How can you change an object’s state
of motion?
4 Newton’s First Law of Motion—Inertia
4.6 Net Force
A force is needed to change an object’s
state of motion.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
What forces act on a book lying at rest on a table?
• One is the force due to gravity—the weight of the book.
• There must be another force acting on it to produce a net
force of zero—an upward force opposite to the force of
gravity.
The upward force that balances the weight of an object on a
surface is called the support force.
A support force is often called the normal force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The table pushes up on
the book with as much
force as the downward
weight of the book.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The table supports the book with a support force—
the upward force that balances the weight of an object
on a surface.
A support force is often called the normal force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
• The upward support force is positive and the downward
weight is negative.
• The two forces add mathematically to zero.
• Another way to say the net force on the book is zero is
F = 0.
The book lying on the table compresses atoms in the table and
they squeeze upward on the book. The compressed atoms
produce the support force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The upward support
force is as much as the
downward pull of
gravity.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The upward support
force is as much as the
downward pull of
gravity.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
What is the net force on a bathroom scale when a 110-pound
person stands on it?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
What is the net force on a bathroom scale when a 110-pound
person stands on it?
Answer: Zero–the scale is at rest. The scale reads the
support force, not the net force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
Suppose you stand on two bathroom scales with your weight
evenly distributed between the two scales. What is the reading
on each of the scales? What happens when you stand with
more of your weight on one foot than the other?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
Suppose you stand on two bathroom scales with your weight
evenly distributed between the two scales. What is the reading
on each of the scales? What happens when you stand with
more of your weight on one foot than the other?
Answer: In the first case, the reading on each scale is half
your weight. In the second case, if you lean more on one
scale than the other, more than half your weight will be read
on that scale but less than half on the other. The total support
force adds up to your weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
For an object at rest on a horizontal surface,
what is the support force equal to?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
For an object at rest on a horizontal surface, the
support force must equal the object’s weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
Mechanical equilibrium is a state wherein no physical
changes occur.
Whenever the net force on an object is zero, the object
is in mechanical equilibrium—this is known as the
equilibrium rule.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
• The  symbol stands for “the sum of.”
• F stands for “forces.”
For a suspended object at rest, the forces acting upward on
the object must be balanced by other forces acting downward.
The vector sum equals zero.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the
downward vectors. F = 0, and the scaffold is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the
downward vectors. F = 0, and the scaffold is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the
downward vectors. F = 0, and the scaffold is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The sum of the upward vectors equals the sum of the
downward vectors. F = 0, and the scaffold is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
If the gymnast hangs with her weight evenly
divided between the two rings, how would scale
readings in both supporting ropes compare with
her weight? Suppose she hangs with slightly
more of her weight supported by the left ring.
How would a scale on the right read?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
If the gymnast hangs with her weight evenly
divided between the two rings, how would scale
readings in both supporting ropes compare with
her weight? Suppose she hangs with slightly
more of her weight supported by the left ring.
How would a scale on the right read?
Answer: In the first case, the reading on each
scale will be half her weight. In the second case,
when more of her weight is supported by the left
ring, the reading on the right reduces to less
than half her weight. The sum of the scale
readings always equals her weight.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
How can you express the equilibrium
rule mathematically?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
You can express the equilibrium rule
mathematically as F = 0.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
The state of rest is only one form of equilibrium.
An object moving at constant speed in a straight-line path is
also in a state of equilibrium. Once in motion, if there is no net
force to change the state of motion, it is in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
An object under the influence of only one force cannot
be in equilibrium.
Only when there is no force at all, or when two or more
forces combine to zero, can an object be in equilibrium.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
When the push on the
desk is the same as the
force of friction between
the desk and the floor,
the net force is zero
and the desk slides at
an unchanging speed.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
If the desk moves steadily at constant speed, without change
in its motion, it is in equilibrium.
• Friction is a contact force between objects that slide or
tend to slide against each other.
• In this case, F = 0 means that the force of friction is
equal in magnitude and opposite in direction to the
pushing force.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
An airplane flies horizontally at constant speed in a straightline direction. Its state of motion is unchanging. In other
words, it is in equilibrium. Two horizontal forces act on the
plane. One is the thrust of the propeller that pulls it forward.
The other is the force of air resistance (air friction) that acts in
the opposite direction. Which force is greater?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
think!
An airplane flies horizontally at constant speed in a straightline direction. Its state of motion is unchanging. In other
words, it is in equilibrium. Two horizontal forces act on the
plane. One is the thrust of the propeller that pulls it forward.
The other is the force of air resistance (air friction) that acts in
the opposite direction. Which force is greater?
Answer: Neither, for both forces have the same strength. Call
the thrust positive. Then the air resistance is negative. Since
the plane is in equilibrium, the two forces combine to equal
zero.
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
How are static and dynamic
equilibrium different?
4 Newton’s First Law of Motion—Inertia
4.7 Equilibrium – When Net Force Equals Zero
Objects at rest are said to be in static equilibrium;
objects moving at constant speed in a straight-line
path are said to be in dynamic equilibrium.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The sum of two or more vectors is called their resultant.
Combining vectors is quite simple when they are parallel:
• If they are in the same direction, they add.
• If they are in opposite directions, they subtract.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
a. The tension in the rope
is 300 N, equal to
Nellie’s weight.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
a. The tension in the rope
is 300 N, equal to
Nellie’s weight.
b. The tension in each rope
is now 150 N, half of
Nellie’s weight. In each
case, F = 0.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The Parallelogram Rule
To find the resultant of nonparallel vectors, we use the
parallelogram rule.
Consider two vectors at right angles to each other, as shown
below. The constructed parallelogram in this special case is a
rectangle. The diagonal is the resultant R.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
The Parallelogram Rule
In the special case of two perpendicular vectors that are equal
in magnitude, the parallelogram is a square.
The resultant is times one of the vectors.
For example, the resultant of two equal vectors of magnitude
100 acting at a right angle to each other is 141.4.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When Nellie is suspended at
rest from the two non-vertical
ropes, is the rope tension
greater or less than the
tension in two vertical ropes?
You need to use the
parallelogram rule to
determine the tension.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Notice how the tension vectors form a parallelogram in which
the resultant R is vertical.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
Nellie’s weight is shown by the downward vertical vector.
An equal and opposite vector is needed for equilibrium, shown by the dashed
vector. Note that the dashed vector is the diagonal of the parallelogram defined by
the dotted lines.
Using the parallelogram rule, we find that the tension in each rope is more than half
her weight.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
As the angle between the ropes increases, tension increases so that the
resultant (dashed-line vector) remains at 300 N upward, which is required
to support 300-N Nellie.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
When the ropes supporting Nellie are at different angles to the vertical, the
tensions in the two ropes are unequal.
By the parallelogram rule, we see that the right rope bears most of the load
and has the greater tension.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
Applying the Parallelogram Rule
You can safely hang from a clothesline hanging vertically, but
you will break the clothesline if it is strung horizontally.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Two sets of swings
are shown at right.
If the children on the
swings are of equal
weights, the ropes of
which swing are more likely to break?
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Two sets of swings
are shown at right.
If the children on the
swings are of equal
weights, the ropes of
which swing are more likely to break?
Answer: The tension is greater in the ropes hanging at an
angle. The angled ropes are more likely to break than the
vertical ropes.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Consider what would happen if you suspended a 10-N object
midway along a very tight, horizontally stretched guitar string.
Is it possible for the string to remain horizontal without a slight
sag at the point of suspension?
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
think!
Consider what would happen if you suspended a 10-N object
midway along a very tight, horizontally stretched guitar string.
Is it possible for the string to remain horizontal without a slight
sag at the point of suspension?
Answer: No way! If the 10-N load is to hang in equilibrium,
there must be a supporting 10-N upward resultant. The
tension in each half of the guitar string must form a
parallelogram with a vertically upward 10-N resultant.
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
How can you find the resultant of
two vectors?
4 Newton’s First Law of Motion—Inertia
4.8 Vector Addition of Forces
To find the resultant of two vectors, construct a
parallelogram wherein the two vectors are
adjacent sides. The diagonal of the
parallelogram shows the resultant.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Copernicus announced the idea of a moving Earth in the
sixteenth century. One of the arguments against a moving
Earth was:
• Consider a bird sitting at rest in the top of a tall tree.
• The bird sees a worm, drops down vertically, and
catches it.
• It was argued that this would not be possible if Earth
moved as Copernicus suggested.
• The fact that birds do catch worms from high tree
branches seemed to be clear evidence that Earth must
be at rest.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Objects Move With Earth
You can refute this argument using the idea of inertia.
Earth moves at 30 km/s, but so do the tree, the worm
below, and even the air in between.
Objects on Earth move with Earth as Earth moves
around the sun.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Earth does not need to
be at rest for the bird to
catch the worm.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Objects Move With Vehicles
If we flip a coin in a high-speed car, bus, or plane, we
can catch the vertically moving coin as we would if the
vehicle were at rest.
We see evidence for the law of inertia when the
horizontal motion of the coin before, during, and after the
catch is the same.
The vertical force of gravity affects only the vertical
motion of the coin.
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
Flip a coin in an airplane, and
it behaves as if the plane
were at rest. The coin keeps
up with you—inertia in action!
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
4 Newton’s First Law of Motion—Inertia
4.9 The Moving Earth Again
How does the law of inertia apply to
objects in motion?
4 Newton’s First Law of Motion—Inertia
4.9 Mass—A Measure of Inertia
The law of inertia states that objects in
motion remain in motion if no unbalanced
forces act on them.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
1.
Two thousand years ago, people thought that Earth did not
move. One major reason for thinking this was that
a. no force was large enough to move the Earth.
b. Earth’s motion would be unnatural.
c. Earth was near the center of the universe.
d. Earth moved in a perfect circle.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
1.
Two thousand years ago, people thought that Earth did not
move. One major reason for thinking this was that
a. no force was large enough to move the Earth.
b. Earth’s motion would be unnatural.
c. Earth was near the center of the universe.
d. Earth moved in a perfect circle.
Answer: A
4 Newton’s First Law of Motion—Inertia
Assessment Questions
2.
According to Aristotle and his followers over centuries, Earth was at
the center of the universe. The first European to effectively challenge
that notion was
a. Copernicus.
b. Galileo.
c. Newton.
d. Einstein.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
2.
According to Aristotle and his followers over centuries, Earth was at
the center of the universe. The first European to effectively challenge
that notion was
a. Copernicus.
b. Galileo.
c. Newton.
d. Einstein.
Answer: A
4 Newton’s First Law of Motion—Inertia
Assessment Questions
3.
Galileo’s conclusions about motion helped advance science because
they were based on
a. experiments rather than philosophical discussions.
b. philosophical discussions rather than experiments.
c. nonmathematical thinking.
d. Aristotle’s theories of motion.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
3.
Galileo’s conclusions about motion helped advance science because
they were based on
a. experiments rather than philosophical discussions.
b. philosophical discussions rather than experiments.
c. nonmathematical thinking.
d. Aristotle’s theories of motion.
Answer: A
4 Newton’s First Law of Motion—Inertia
Assessment Questions
4.
If gravity between the sun and Earth suddenly vanished, Earth would
continue moving in a(n)
a. curved path.
b. straight-line path.
c. outward spiral path.
d. inward spiral path.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
4.
If gravity between the sun and Earth suddenly vanished, Earth would
continue moving in a(n)
a. curved path.
b. straight-line path.
c. outward spiral path.
d. inward spiral path.
Answer: B
4 Newton’s First Law of Motion—Inertia
Assessment Questions
5.
To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter
a. will weigh 10 N everywhere.
b. has ten times less volume than 10 kg of matter.
c. has ten times more inertia than 10 kg of matter.
d. is attracted to Earth with 10 N of force.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
5.
To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter
a. will weigh 10 N everywhere.
b. has ten times less volume than 10 kg of matter.
c. has ten times more inertia than 10 kg of matter.
d. is attracted to Earth with 10 N of force.
Answer: D
4 Newton’s First Law of Motion—Inertia
Assessment Questions
1.
When you hold a rock in your hand at rest,
the forces on the rock
a. are mainly due to gravity.
b. are mainly due to the upward push of
your hand.
c. cancel to zero.
d. don’t act unless the rock is dropped.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
1.
When you hold a rock in your hand at rest,
the forces on the rock
a. are mainly due to gravity.
b. are mainly due to the upward push of
your hand.
c. cancel to zero.
d. don’t act unless the rock is dropped.
Answer: C
4 Newton’s First Law of Motion—Inertia
Assessment Questions
2.
Burl and Paul have combined weights of 1300 N. The tensions in
the supporting ropes that support the scaffold they stand on add to
1700 N. The weight of the scaffold itself must be
a.
b.
c.
d.
400 N.
500 N.
600 N.
3000 N.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
2.
Burl and Paul have combined weights of 1300 N. The tensions in
the supporting ropes that support the scaffold they stand on add to
1700 N. The weight of the scaffold itself must be
a.
b.
c.
d.
Answer: A
400 N.
500 N.
600 N.
3000 N.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
3.
Harry gives his little sister a piggyback ride. Harry weighs 400 N and
his little sister weighs 200 N. The support force supplied by the floor
must be
a. 200 N.
b. 400 N.
c. 600 N.
d. more than 600 N.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
3.
Harry gives his little sister a piggyback ride. Harry weighs 400 N and
his little sister weighs 200 N. The support force supplied by the floor
must be
a. 200 N.
b. 400 N.
c. 600 N.
d. more than 600 N.
Answer: C
4 Newton’s First Law of Motion—Inertia
Assessment Questions
4.
When a desk is horizontally pushed across a floor at a steady speed
in a straight-line direction, the amount of friction acting on the desk is
a. less than the pushing force.
b. equal to the pushing force.
c. greater than the pushing force.
d. dependent on the speed of the sliding crate.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
4.
When a desk is horizontally pushed across a floor at a steady speed
in a straight-line direction, the amount of friction acting on the desk is
a. less than the pushing force.
b. equal to the pushing force.
c. greater than the pushing force.
d. dependent on the speed of the sliding crate.
Answer: B
4 Newton’s First Law of Motion—Inertia
Assessment Questions
5.
When Nellie hangs at rest by a pair of ropes, the tensions in the
ropes
a. always equal her weight.
b. always equal half her weight.
c. depend on the angle of the ropes to the vertical.
d. are twice her weight.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
5.
When Nellie hangs at rest by a pair of ropes, the tensions in the
ropes
a. always equal her weight.
b. always equal half her weight.
c. depend on the angle of the ropes to the vertical.
d. are twice her weight.
Answer: C
4 Newton’s First Law of Motion—Inertia
Assessment Questions
6.
The Earth moves about 30 km/s relative to the sun. But when you
jump upward in front of a wall, the wall doesn’t slam into you at 30
km/s. A good explanation for why it doesn’t is that
a. the sun’s influence on you is negligible.
b. the air in the room is also moving.
c. both you and the wall are moving at the same speed, before,
during, and after your jump.
d. the inertia of you and the wall is negligible compared with that of
the sun.
4 Newton’s First Law of Motion—Inertia
Assessment Questions
6.
The Earth moves about 30 km/s relative to the sun. But when you
jump upward in front of a wall, the wall doesn’t slam into you at 30
km/s. A good explanation for why it doesn’t is that
a. the sun’s influence on you is negligible.
b. the air in the room is also moving.
c. both you and the wall are moving at the same speed, before,
during, and after your jump.
d. the inertia of you and the wall is negligible compared with that of
the sun.
Answer: C